Extracting stress intensity factors for isotropic cracked domains having stochastic material properties

Abstract

Material properties are inevitably stochastic due to the manufacturing process and the measurement procedure. In case of a cracked domain, the stochasticity of material properties (as stochastic variables) may manifest in the stress intensity factors (SIFs). Having the stochastic representation of the material properties, Young modulus and Poisson ratio (isotropic material), we approximate the SIFs for 2D cracked domains using the generalized polynomial chaos (gPC). The approximated SIF consists of two families of orthogonal polynomials, selected by the probability distribution function of the material properties. The polynomials are multiplied by a deterministic coefficient, consisting of deterministic SIFs, extracted from a finite element model according to the stochastic properties of both Young modulus and Poisson ratio. Numerical example problems are provided where the stochastic approximation of the SIF is computed. The obtained approximation of the SIF is compared with results obtained using the Monte Carlo method. The results demonstrate the efficiency and accuracy of the proposed method.